Taking advantage of this inside information is impeded by the
investor's adverse market impact. Following
[1]}, we model this impact in a temporary linear
form and, thus, when at time \(t\)  the investor turns over her position \(\Phi _t\)  at
the rate \(\phi _t=\dot{\Phi }_t\)  the execution price is \(S_t + \frac{\Lambda }{2}\phi _t\)  for some constant \(\Lambda >0\) . As a result, the profits and
losses from trading are given by
\(V^{\Phi _0,\phi }_T:=\Phi _0(S_T-S_0)+\int _{0}^T \phi _t(S_T-S_t)dt-\frac{\Lambda }{2} \int _{0}^T \phi ^2_t dt,\) 
